Omer Abid, Gholamreza Rafiee * Abstract -- Medulloblastoma is a malignant pediatric brain cancer, and the discovery of molecular subgroups is enabling personalized treatment strategies. In 2019, a consensus identified eight novel subtypes within Groups 3 and 4, each displaying heterogeneous chara cteristics. Classifiers are essential for translating these findings into clinical practice by supporting clinical trials, personalized therapy development and application, and patient monitoring. This study presents a DNA methylation - based, cross - platform machine learning classifier capable of distinguishing these subtypes on both HM450 and EPIC methylation array samples . Across two independent test sets, the model achieved weighted F1 = 0.95 and balanced accuracy = 0.957, consistent across platforms. As the first cross - platform solution, it provides backward compatibility while extending applicability to a newer platform, also enhancing accessibility. It also has the potential to become the first publicly available classifier for these subtypes once deployed through a web application, as planned in the future . Th is work overall takes steps in the direction of advancing precision medicine and improving clinical outcomes for patients within the majority prevalence medulloblastoma subgroups, g roups 3 and 4. Keywords -- Medulloblastoma, Molecular Subgroup Classification, Machine Learning, AI for Health Medulloblastoma is a malignant brain cancer widely known for its prevalence in children. Through extensive treatment strategies based on surgery, chemotherapy and radiation therapy, approximately 75% of the patient are able to survive in the long term [1]. These treatments whi le crucial also come along with negative side effects, effecting patients' li ves [1] [2], especially considering the implications on the growing children. However, with advancement in genomics, molecular subgroups have been discover ed within the disease . T hese subgroups have shown to be heterogenous in clinical, biological and outcomes perspective [3] . These in fact are now considered better definition of disease behaviour than conventional techniques [3] .

Direct Preference Optimization (DPO) has emerged as a compelling approach for training Large Language Models (LLMs) to adhere to human preferences. However, the performance of DPO is sensitive to the fine-tuning of its trade-off parameter \beta, as well as to the quality of the preference data. We analyze the impact of \beta and data quality on DPO, uncovering that optimal \beta values vary with the informativeness of pairwise data. Addressing the limitations of static \beta values, we introduce a novel framework that dynamically calibrates \beta at the batch level, informed by data quality considerations. Additionally, our method incorporates \beta -guided data filtering to safeguard against the influence of outliers. Through empirical evaluation, we demonstrate that our dynamic \beta adjustment technique significantly improves DPO's performance across a range of models and datasets, offering a more robust and adaptable training paradigm for aligning LLMs with human feedback.

Large language models have transformed AI, yet reliably controlling their outputs remains a challenge. This paper explores activation engineering, where outputs of pre-trained LLMs are controlled by manipulating their activations at inference time. Unlike traditional methods using a single steering vector, we introduce conceptors - mathematical constructs that represent sets of activation vectors as ellipsoidal regions. Conceptors act as soft projection matrices and offer more precise control over complex activation patterns. Our experiments demonstrate that conceptors outperform traditional methods across multiple steering tasks. We further use Boolean operations on conceptors for combined steering goals that empirically outperform additively combining steering vectors on a set of tasks. These results highlight conceptors as a promising tool for more effective steering of LLMs. Our code is available on github.com/jorispos/conceptorsteering.

The advent of Large Language Models (LLMs) has altered the Natural Language Processing (NLP) landscape, empowering professionals across diverse disciplines with their remarkable ability to generate human-like text. Models like OpenAI's GPT [44], Meta's Llama [45], and Anthropic's Claude 3 [4] have become indispensable collaborators in many peoples' daily lives; giving rise to innovative products such as ChatGPT for general use, GitHub Copilot for code generation, DALL-E 2 for image creation, and a multitude of voice generators, including OpenAI's text-to-speech API and ElevenLabs's Generative Voice AI. Currently, LLMs are being experimentally applied across various fields, yielding mixed results [3]. While some applications seem questionable, others exhibit spectacular outcomes. One of the most contentious applications is using LLMs for tasks necessitating mathematical reasoning. Given LLMs' inherently probabilistic nature, this application was once deemed implausible. However, recent findings suggest a shift in perspective, particularly with LLMs boasting vast parameter counts [1]. As LLMs continue to scale, new capabilities emerge [48]. Crucially, these opportunities are contingent upon the thoughtful design of prompts, which helps mitigate the risk of LLMs providing irrelevant or inaccurate responses [47]. 1

The capital asset pricing model (CAPM) is very widely used and is considered to be a very fundamental concept in investing. It determines the link between the risk and expected return of assets, in particular stocks. According to CAPM, the value of α is expected to be zero and that it is very random and cannot be predicted. The equation seen above is in the form of y mx b and therefore it can be treated as a form of linear regression. The scipy package will be used. It has a function to calculate the linear regression.

Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching provides a powerful tool for estimating densities with such intractable normalizing constants, but as originally proposed is limited to densities on $\mathbb{R}^m$ and $\mathbb{R}_+^m$. In this paper, we offer a natural generalization of score matching that accommodates densities supported on a very general class of domains. We apply the framework to truncated graphical and pairwise interaction models, and provide theoretical guarantees for the resulting estimators. We also generalize a recently proposed method from bounded to unbounded domains, and empirically demonstrate the advantages of our method.

In addition to seamless connectivity and smartness, the objects in the Internet of Things (IoT) are expected to have the social capabilities -- these objects are termed as ``social objects''. In this paper, an intuitive paradigm of social interactions between these objects are argued and modeled. The impact of social behavior on the interaction pattern of social objects is studied taking Peer-to-Peer (P2P) resource sharing as an example application. The model proposed in this paper studies the implications of competitive vs. cooperative social paradigm, while peers attempt to attain the shared resources / services. The simulation results divulge that the social capabilities of the peers impart a significant increase in the quality of interactions between social objects. Through an agent-based simulation study, it is proved that cooperative strategy is more efficient than competitive strategy. Moreover, cooperation with an underpinning on real-life networking structure and mobility does not negatively impact the efficiency of the system at all; rather it helps.

Minimax, as the name suggest, is a method in decision theory for minimizing the maximum loss. Alternatively, it can be thought of as maximizing the minimum gain, which is also know as Maximin. It all started from a two player zero-sum game theory, covering both the cases where players take alternate moves and those where they made simultaneous moves. It has also been extended to more complex games and to general decision making in the presence of uncertainty. In the above explanation, it has been mentioned that the minimax algorithms started off with the concept of zero-sum.

Dept. of Computer Science, Carnegie-Mellon University. "Many game-playing programs must search very large game trees. Use of the alpha-beta pruning algorithm instead of the simple minimax search reduces by a large factor the number of bottom positions which must be examined in the search. An analytical expression for the expected number of bottom positions examined in a game tree using alpha-beta pruning is derived, subject to the assumptions that the branching factor N and the depth D of the tree are arbitrary but fixed, and the bottom positions are a random permutation of ND unique values. A simple approximation to the growth rate of the expected number of bottom positions examined is suggested, based on a Monte Carlo simulation for large values of N and D. The behavior of the model is compared with the behavior of the alpha-beta algorithm in a chess playing program and the effects of correlation and non-unique bottom position values in real game trees are examined."